The Lipschitz bandit is a key variant of stochastic bandit problems where the expected reward function satisfies a Lipschitz condition with respect to an arm metric space. With its wide-ranging practical applications, various Lipschitz bandit algorithms have been developed, achieving the optimal regret performance in the classical setting. Motivated by recent advancements in quantum computing and the demonstrated success of quantum Monte Carlo in simpler bandit settings, we introduce the first quantum Lipschitz bandit algorithms to address the challenges of continuous action spaces and non-linear reward functions. Specifically, we first leverage the elimination-based framework to propose an efficient quantum Lipschitz bandit algorithm named Q-LAE. Next, we present novel modifications to the classical Zooming algorithm, which results in a simple quantum Lipschitz bandit method, Q-Zooming. Both algorithms exploit the computational power of quantum methods to obtain a provably improved regret bound over classical Lipschitz bandit algorithms. Comprehensive experiments further validate our improved theoretical findings, demonstrating superior empirical performance compared to existing Lipschitz bandit methods.

As deep neural networks can easily overfit noisy labels, robust training in the presence of noisy labels is becoming an important challenge in modern deep learning. While existing methods address this problem in various directions, they still produce unpredictable sub-optimal results since they rely on the posterior information estimated by the feature extractor corrupted by noisy labels. Lipschitz regularization successfully alleviates this problem by training a robust feature extractor, but it requires longer training time and expensive computations. Motivated by this, we propose a simple yet effective method, called ALASCA, which efficiently provides a robust feature extractor under label noise. ALASCA integrates two key ingredients: (1) adaptive label smoothing based on our theoretical analysis that label smoothing implicitly induces Lipschitz regularization, and (2) auxiliary classifiers that enable practical application of intermediate Lipschitz regularization with negligible computations. We conduct wide-ranging experiments for ALASCA and combine our proposed method with previous noise-robust methods on several synthetic and real-world datasets. Experimental results show that our framework consistently improves the robustness of feature extractors and the performance of existing baselines with efficiency.